A Functional Approach to Solubility Parameter Computations.

The determination of solubility parameters for solutes represents a challenging mathematical problem of locating the central tendency of solvent affinity based on a limited set of data taken from experimental observations. At present, the most commonly used methods for computing solubility parameters of a solute require a binary classification of solvent affinity for the solute and employ a spherical/ellipsoidal compatibility region in the three-dimensional Hansen solubility parameter space. Utilizing a binary classification requires an arbitrary solubility threshold, and an ellipsoidal fitting model imposes a symmetry on the intermolecular forces that is rarely reflected by the experimental data. To overcome these issues, an approach that makes use of accurate solubility data to describe a three-dimensional solubility function, f, is introduced. The principles of the approach are discussed in detail and the procedures for constructing the solubility function and computing solubility parameters are described. An example using PCBM solubility data available in the literature demonstrates the new method. Lastly, a method that employs f as a predictor of solubility in arbitrary solvents with a proposed measure of reliability is presented.